Source : http://www-irma.u-strasbg.fr/~foata/paper

Dominique Foata

List of Publications (May 14, 2011)

• 118. (with Guoniu Han) Doubloons and q-secant numbers, Münster J. of Math. 3 (2010), 129-150

• 117. Eulerian Polynomials: from Euler's Time to the Present, Invited address at the 10-th Annual Ulam Colloquium, University of Florida, February 18, 2008. Published in "The Legacy of Alladi Ramakrishnan in the Mathematical Sciences," K. Alladi, J.R. Klauder, C.R. Rao, eds., Springer, New York Dordrecht Heidelberg London, 2010, p. 253-273.

• 116b. (with Guoniu Han) The Flag-Descent and -Excedance Numbers, on line, 7 p.

• 116a. (with Guoniu Han) A Wreath Product Multivariable Extension, on line, 6 p.

• 116. (with Guoniu Han) The Decrease Value Theorem with an Application to Permutation Statistics, Advances in Applied Mathematics (Special issue in honor of Dennis Stanton; edited by Mourad E.H. Ismail, Erik Koelink and Victor Reiner) 46, Issues 1-4 (2011), 296-311.

• 115. (with Guoniu Han) The (t,q)-analogs of Secant and Tangent numbers, Electronic J. Combin. Vol. 18 (2) (May 13, 2011) (The Zeilberger Festschrift), P7, 16 p.

• 114. (with Guoniu Han) New permutation coding and equidistribution of set-valued statistics, Theoretical Computer Science, 410 (38), 2009, p. 3743-3750.

• 113. Les polynômes Eulériens, d'Euler à Carlitz, read at the conference "Leonhard Euler, mathématicien, physicien et théoricien de la musique," IRMA Strasbourg, november 15-16, 2007, X. Hascher and A. Papadopoulos, org., 18 p.

• 112. (with Guoniu Han) The doubloon polynomial triangle, Ramanujan Journal, Vol. 23, Nos. 1-3, December 2010, p. 107-126.

• 111. (with Guoniu Han) Doubloons and new q-tangent numbers, Quarterly J. Math., 62(2), 2011, p. 417-432; first published online December 19, 2009 doi:10.1093/qmath/hap043

• 110. (with Guoniu Han) The q-tangent and q-secant numbers via basic Eulerian polynomials, Proceedings of the American Mathematical Society, volume 138 (2010), no. 2, 385-393.

• 109. (with Guoniu Han) Statistical Distributions on Words and q-Calculus on Permutations, a 194-page volume, containing the papers "Signed words and permutations, I-V", "Fix-Mahonian Calculus, I-III", paper 108 and a joint paper by Han and Xin, Strasbourg, September 2007

• 108. (with Guoniu Han) Decreases and Descents in Words, Séminaire Lotharingien de Combinatoire, B58a (2007), 17 pp.

• 107. (with Guoniu Han) Signed words and permutations, V; a sextuple distribution, Ramanujan J., Volume 19, Issue 1, May 2009, p. 29-52

• 106. (with Guoniu Han) Fix-Mahonian Calculus, III: a quadruple distribution, Monatshefte für Mathematik, 154, 2008, p. 177-197.

• 105. (with Guoniu Han) Fix-Mahonian Calculus, II: further statistics, Journal of Combinatorial Theory, Series A, Volume 115, Issue 5, July 2008, p. 726-736.

• 104. (with Guoniu Han) Fix-Mahonian Calculus, I: two transformations, Europ. J. Combin., 29, 2008, 1721-1732.

• 103. (with M.-P. Schützenberger, made available on the web by Jean Berstel) Quelques remarques sur une propriété d'équidistribution des permutations, Analyse appliquée et informatique, Journées de combinatoire, 4-6 juin 1975 [Jean-Claude Bermond et Robert Cori, eds.], Labo. assoc. 226, U.E.R Math. Info., Bordeaux 1, p. 121-124.

• 102. (with Guoniu Han) Signed words and permutations, IV; fixed and pixed points , Israel J. Math., 163, no. 1, 2008, p. 217-240.

• 101. (with Guoniu Han) Specializations and Extensions of the quantum MacMahon Master Theorem , Linear Algebra and its Applications, 423, 2007, p. 445-455.

• 100. (with Guoniu Han) A New Proof of the Garoufalidis-Le-Zeilberger Quantum MacMahon Master Theorem, Journal of Algebra, 307, Issue 1, 2007, p. 424-431.

• 99. (with Guoniu Han) A basis for the right quantum algebra and the ``1=q" principle, J. Algebraic Combinatorics, 27, No. 2, 2008, p. 163-172.

• 98. (with Guoniu Han) Signed words and permutations, III: the MacMahon Verfahren, Séminaire Lotharingien de Combinatoire, vol. 54a, 2006, 20 pages (The Viennot Festschrift).

• 97. (with Guoniu Han) Signed words and permutations, II: the Euler-Mahonian polynomials, Electronic J. Combinatorics, 11(2), #R22, 2005, 18 pages (The Stanley Festschrift).

• 96. (with Arthur Randrianarivony) Two Oiseau Decompositions of Permutations and their Application to Eulerian Calculus, Europ. J. Combinatorics, 27, 2006, p. 342-363.

• 95. Random Permutations and Bernoulli Sequences, 10 pages

• 94. Une méthode combinatoire pour l'étude des fonctions spéciales Journées sur les méthodes mathématiques, Institut Henri Poincaré, Paris, 2-3 avril 2003. Published in Math. Sci. Hum. Math. Soc. Sci., 179, 2007, p. 85-99.

• 93. The Lotharingian Impact on Combinatorial Mathematics: myth or reality? Séminaire Lotharingien de Combinatoire, vol. 50, 2003, B50a (15 pages).

• 92. (with Guoniu Han) Signed words and permutations, I: a fundamental transformation, Proceedings of the American Mathematical Society, 135, 2007, no. 1, 31-40.

• 91. (with Guoniu Han) q-series in Combinatorics; permutation statistics (Lecture Notes).

• 90. (with Guoniu Han) Une nouvelle transformation pour les statistiques Euler-mahoniennes ensemblistes, Moscow Mathematical Journal (issue dedicated to Pierre Cartier), 4, 2004, p. 131-152.

• 89. (with Doron Zeilberger) The Collector's Brotherhood Problem Using the Newman-Shepp Symbolic Method, Algebra Universalis (special Rota memorial issue), 49, 2003, p. 387-395

• 88. (with Guoniu Han and Bodo Lass) Les nombres hyperharmoniques et la fratrie du collectionneur de vignettes, Séminaire Lotharingien de Combinatoire, vol. 47, B47a, 2001, 20 pages.

• 87. (with Guoniu Han) (Eds.) The Andrews Festschrift. Seventeen Papers on Classical Number Theory and Combinatorics, Springer-Verlag, Berlin Heidelberg, 2001.

• 86. (with Guoniu Han) Arbres minimax et polynômes d'André, Advances in Appl. Math., 27, 2001, p. 367-389.

• 85. (with Doron Zeilberger) Babson-Steingrímsson Statistics Are Indeed Mahonian (and Sometimes Even Euler-Mahonian), Advances in Appl. Math., 27, 2001, p. 390-404.

• 84. (with GuoNiu Han) The Triple, Quintuple and Septuple Product Identities Revisited, Séminaire Lotharingien de Combinatoire, vol. 42, B42o, 1999, 12 p. (The Andrews Festschrift)

• 83. (with GuoNiu Han) Word straightening and q-Eulerian Calculus, Contemporary Mathematics, vol. 254, q-Series from a Contemporary Perspective, p. 141-156, [AMS-IMS-SIAM Joint Summer Research Conference on q-series, Combinatorics, and Computer Algebra, in honor of Richard Askey, June 21-25, 1998, Mount Holyoke College, South Hadley, MA; Mourad E.H. Ismail, Dennis W. Stanton, eds.], 2000, Providence, Amer. Math. Soc.

• 82. (with GuoNiu Han) Inverses of Words, Séminaire Lotharingien de Combinatoire, B39d, 1997, 8pp.

• 81. (with GuoNiu Han) Jacobi and Watson Identities Combinatorially Revisited, 16 pp. Home page only.

• 80. (with GuoNiu Han) Transformations on Words and q-Calculus, Algebraic Combinatorics on Words, 10th chapter, pp. 293-324, Cambridge Univ. Press, 2001.

• 79. (with GuoNiu Han) Transformations on Words, J. of Algorithms, 28, 1998, p. 172-191.

• 78. (with Doron Zeilberger) A combinatorial proof of Bass's evaluations of the Ihara-Selberg Zeta function for graphs, Trans. Amer. Math. Soc., 351, 1999, p. 2257-2274.

• 77. (with Doron Zeilberger) A classic proof of a recurrence for a very classical sequence, J. Combinatorial Theory, ser. A, 80, 1997, p. 380-384.

• 76. (with Guo Niu Han) Calcul basique des permutations signées, II: analogues finis des fonctions de Bessel, The Electronic J. Combinatorics, 4 (2), 1997, R9 (The Herb Wilf Festschrift).

• 75. (with Guo Niu Han) Calcul basique des permutations signées, I: longueur et nombre d'inversions, Advances in Appl. Math., 18, 1997, p. 489-509.

• 74. (with Christian Krattenthaler) Graphical Major Indices, II, Séminaire Lotharingien de Combinatoire, B34k, 1994, 16 pp.

• 73. (with Doron Zeilberger) Graphical Major Indices, J. of Computational and Applied Math., 68, 1996, p. 79-101.

• 72. (with Robert J. Clarke) Eulerian Calculus, IV: specializations, Séminaire Lotharingien de Combinatoire, B32b, 1994, 12pp.

• 71. (with Guo Niu Han) Nombres de Fibonacci et polynômes orthogonaux, Leonardo Fibonacci: il tempo, le opere, l'ereditá scientifica [Pisa. 23-25 Marzo 1994, Marcello Morelli e Marco Tangheroni, ed.], p. 179-200. Pisa, Pacini Editore (Fondazione IBM Italia), 1994.

• 70. (with Robert J. Clarke) Eulerian Calculus, III : The Ubiquitous Cauchy Formula, Europ. J. Combinatorics, 16, 1995, p. 329-355.

• 69. (with Robert J. Clarke) Eulerian Calculus, II: An Extension of Han's Fundamental Transformation, Europ. J. Combinatorics, 16, 1995, p. 221-252.

• 68. (with Robert J. Clarke) Eulerian Calculus, I: Univariable Statistics, Europ. J. Combinatorics, 15, 1994, p. 345-362.

• 67. Commutation et réarrangements, hier et aujourd'hui, Actes de la R.C.P. no. 25, Rencontre entre physiciens théoriciens et mathématiciens (GDR 859) [Strasbourg, mai 1992], colloque en hommage à Pierre Cartier, vol. 44, p. 25-37, Prépubl. I.R.M.A. Strasbourg, 1993, 041.

• 66. Les distributions Euler-Mahoniennes sur les mots, Discrete Math., 139, 1995, p. 167-188.

• 65. (with Doron Zeilberger) Combinatorial Proofs of Capelli's and Turnbull's identities from Classical Invariant Theory, Electronic J. Combinatorics, 1, 1994, R1.

• 64. (with Doron Zeilberger) Multibasic Eulerian polynomials, Trans. Amer. Math. Soc., 328, 1991, p. 843-862.

• 63. (with Doron Zeilberger) Denert's permutation statistic is indeed Euler-Mahonian, Studies in Appl. Math., 83, 1990, 31-59.

• 62. (with Jacques Désarménien) The signed Eulerian Numbers, Discrete Math., 99, 1992, p. 49-58.

• 61. (with Doron Zeilberger) Linearization Coefficients for the Jacobi Polynomials, Séminaire Lotharingien de combinatoire (Bayreuth, Erlangen, Strasbourg), 16e session, p. 73-86, Publ. IRMA Strasbourg, 341/S--16, 1987. [Electronically reprinted as: B16a, 1987, 14pp.]

• 60. (with Jacques Désarménien) Statistiques d'ordre sur les permutations colorées, Discrete Math., 87, 1991, p. 133-148.

• 59. (with Doron Zeilberger) Laguerre polynomials, weighted derangements and positivity, SIAM J. Discrete Math., 1, 1988, p. 425-433.

• 58. Permutations colorées et tableaux gauches, Mots, Mélanges offerts à M.-P. Schützenberger, (A. Lascoux and D. Perrin, eds.), Hermès, Paris, 1990, p. 208-220.

• 57. (with Jacques Désarménien) Fonctions symétriques et séries hypergéométriques basiques multivariées, II, Combinatoire Enumérative [Montréal. 28 mai-1er juin 1985, G. Labelle et P. Leroux, eds.], p. 68-90. Berlin, Springer-Verlag, 1986 (Lecture Notes in Math., 1234).

• 56. (with Doron Zeilberger) Weighted derangements and Laguerre polynomials, Séminaire Lotharingien de combinatoire, 8e session, p. 17-25. Publ. IRMA Strasbourg, 229/S-08, 1984. [Electronically reprinted as: B08c, 1983, 9pp.]

• 55. (with Yves Roy) TEX/SM 90, Publ. I.R.M.A. Strasbourg 258/D--07, jan. 1985, 84 pages.

• 54. (with Jean-Jacques Pansiot and Yves Roy) Stratec and a rationalized keyboard for inputting TeX, Proc. First Europ. Conf. on TeX for scientific documentation [Como. 16--17 May 1985, D. Lucarella, ed.], p. 105-116. Reading, Mass., Addison-Wesley, 1985.

• 53. (with Jacques Désarménien) Fonctions symétriques et séries hypergéométriques basiques multivariées, Bull. Soc. Math. France, 113, 1985, p. 3-22.

• 52. La combinatoire classique, Gazette des Mathématiciens, S.M.F., 25, sept. 1984, p. 173-185.

• 51. Combinatoire des identités sur les polynômes orthogonaux, Proc. Internat. Congress of Math. [Warsaw. August 16-24, 1983], vol. 2, p. 1541-1553. Warszawa, PWN - Polish Scientific Publications and Amsterdam, North-Holland, 1984.

• 50. Une démonstration combinatoire de l'identité de Pfaff-Saalschütz, C.R. Acad. Sc. Paris, 297, 1983, p. 221-224.

• 49. TeX à Strasbourg, Gazette des Mathématiciens, S.M.F., 21, mars 1983, p. 89-97.

• 48. Combinatoire des identités sur les polynômes de Meixner, Séminaire Lotharingien de combinatoire, 6e session, p. 114-128. Publ. IRMA Strasbourg, 191/S-05, 1982. [Electronically reprinted as : B06c, 11pp.]

• 47. (with Volker Strehl) Combinatorics of Laguerre polynomials, Enumeration and Design [Waterloo. June-July 1982; D.M. Jackson and S.A. Vanstone, eds.], p. 123-140. Toronto, Academic Press, 1984.

• 46. La mathématique combinatoire, Gazette des Sciences Mathématiques du Québec, 6, no. 3, mars 1982, p. 8-16.

• 45. (with Jacques Labelle) Modèles combinatoires pour les polynômes de Meixner, Europ. J. Combinatorics, 4, 1983, p. 305-311.

• 44. (with Pierre Leroux) Polynômes de Jacobi, interprétation combinatoire et fonction génératrice, Proc. Amer. Math. Soc., 87, 1983, p. 47-53.

• 43. Rearrangements of words, Combinatorics on words [M. Lothaire, ed.], p. 184-212. Reading, Massachusetts, Addison-Wesley, 1983 (Encyclopedia of Math. and its Appl., 17).

• 42. (with Volker Strehl) Une extension multilinéaire de la formule d'Erdélyi pour les produits de fonctions hypergéométriques confluentes, C.R. Acad. Sc. Paris, 293, 1981, p. 517-520.

• 41. Aspects combinatoires du calcul des q-séries, Séminaire d'Informatique Théorique, 1980-81, Laboratoire d'Informatique Théorique et Programmation, Université de Paris VII, p. 37-55.

• 40. Some Hermite polynomial identities and their combinatorics, Advances in Appl. Math., 2, 1981, 250-259.

• 39. (with George Andrews) Congruences for the q-secant numbers, Europ. J. Combinatorics, 1, 1980, 283-287.

• 38. Further divisibility of the q-tangent numbers, Proc. Amer. Math. Soc., 81, 1981, 143-148.

• 37. (with M.-P. Schützenberger) H.O. Foulkes, édition de son dernier article, Discrete Math., 30, 1980, 1.

• 36. (with Alun O. Morris and H. Perfect) H.O. Foulkes (Obituary), Bull. London Math. Soc., 30, 1979, 208-214.

• 35. A combinatorial proof of Jacobi's identity, Combinatorial Mathematics, Optimal Designs and their Applications [Fort Collins. 1978; J.N. Srivastava, ed.], p. 125-135. Amsterdam, North-Holland, 1980 (Annals Discrete Math., vol. 6).

• 34. A Noncommutative Version of the Matrix Inversion Formula, Adv. in Math., 31, 1979, 330-349.

• 33. A matrix-analog for Viennot's construction of the Robinson correspondence, J. Linear and Multilinear Algebra, 7, 1979, 330-349.

• 32. (with Adriano Garsia) A combinatorial approach of the Mehler formulas for Hermite polynomials, (Relations between Combinatorics and other parts of Mathematics) [1978. Columbus], p. 163-179. Providence, Amer. Math. Soc., 1979.

• 31. A combinatorial proof of the Mehler formula, J. Combinatorial Theory, Ser. A, 24, 1978, 367-376.

• 30. (with M.-P. Schützenberger) Major Index and Inversion number of Permutations, Math. Nachrichten, 83, 1978, 143-159.

• 29. Une propriété du vidage-remplissage des tableaux de Young, Combinatoire et représentation du groupe symétrique [1976. Strasbourg], p. 121-135. Berlin, Springer-Verlag, 1977 (Lecture Notes in Math., 579).

• 28. Introduction, Combinatoire et représentation du groupe symétrique [1976. Strasbourg], p. 1-7. Berlin, Springer-Verlag, 1977 (Lecture Notes in Math., 579).

• 27. Distributions eulériennes et mahoniennes sur le groupe des permutations, Higher Combinatorics [1976. Berlin, M. Aigner, ed.], p. 27-49. Boston, Dordrecht, 1977.

• 26. (with Dominique Dumont) Une propriété de symétrie des nombres de Genocchi, Bull. Soc. Math. France, 104, 1976, 433-451.

• 25. (with Volker Strehl) Euler numbers and variations of permutations, Colloquio Internazionale sulle Teorie Combinatorie [1973. Roma], vol. 1, p. 119-131. Roma, Accademia dei Lincei, 1976 (Atti dei Convegni, 17).

• 24. Inversions de Möbius, Science Research Council Rencontre, Aberdeen [6-12 July, 1975], 5 p.

• 23. Réarrangements d'applications associés aux nombres de Genocchi, Cahiers Mathématiques, Univ. Sc. Techn. Languedoc, Montpellier, 3, 1974, 113-121.

• 22. (with Volker Strehl) Rearrangements of the symmetric group and enumerative properties of the tangent and secant numbers, Math. Zeitschrift, 137, 1974, 257-264.

• 21. (Monograph) La série génératrice exponentielle dans les problèmes d'énumération, Montréal, Presses de l'Université de Montréal, 1974, 186 pages.

• 20. (with John Riordan) Mappings of acyclic and parking functions, Aequationes Mathematicae, 10, 1974, 10-22.

• 19. (with M.-P. Schützenberger) Nombres d'Euler et permutations alternantes, A survey of Combinatorial Theory} [J.N. Srivastava et al., eds.], p. 173-187. Amsterdam, North-Holland, 1973.

• 18. (with M.-P. Schützenberger, made available on the web by Jean Berstel) Nombres d'Euler et permutations alternantes (unabridged version). Technical Report, University of Florida, 1971, 71 pages.

• 17. Groupes de réarrangements et nombres d'Euler, C.R. Acad. Sc. Paris, 275, 1972, 1147-1150.

• 16. Enumerating k-trees, J. Discrete Math., 1, 1971, 181-186.

• 15. (with M.-P. Schützenberger) On the Principle of Equivalence of Sparre Andersen, Math. Scandinavica, 28, 1971, 308-316.

• 14. (Monograph) (with M.-P. Schützenberger) Théorie géométrique des polynômes eulériens, Berlin, Springer-Verlag, 1970 (Lecture Notes in Math. 138), 94 pages.

• 13. (with M.-P. Schützenberger) On the rook polynomials of Ferrers relations, Combinatorial Theory and Its Applications [P. Erdös et al., eds.], vol. 2, p. 413-436. Amsterdam, North-Holland, 1970.

• 12. (with Aimé Fuchs) Réarrangements de fonctions et dénombrement, J. Combinatorial Theory, 8, 1970, 361-375.

• 11. (Monograph) (with Pierre Cartier) Problèmes combinatoires de commutation et réarrangements, Berlin, Springer-Verlag, 1969 (Lecture Notes in Math., 85), 88 pages.

• 10. On the Netto Inversion Number of a Sequence, Proc. Amer. Math. Soc., 19, 1968, 236-240.

• 09. Propriétés arithmétiques des polynômes d'Euler, Séminaire Delange-Pisot-Poitou (Théorie des Nombres), 1967-68, 20.02-20.13. Secrétariat Mathématique, 11, rue Pierre-et-Marie-Curie, Paris.

• 08. Two new combinatorial correspondences, Inst. Statist. Univ. North Carolina Mimeo Series, 1966 (Proc. NATO Summer School at Royan, 1965).

• 07. (thèse Doct. Etat, Paris) Etude algébrique de certains problèmes d'analyse combinatoire et du calcul des probabilités, Publ. Inst. Statist. Univ. Paris, 14, 1965, 81-241.

• 06. Un théorème combinatoire non commutatif, C.R. Acad. Sc. Paris, 258, 1964, 5128-5130.

• 05. Sur un théorème de MacMahon, C.R. Acad. Sc. Paris, 258, 1964, 1672-1675.

• 04. Sur la construction des plans fractionnés factoriels, Publ. Inst. Statist. Univ. Paris, 11, 1962, 57-66.

• 03. A program for Ray-Chaudhuri's algorithm for a minimum cover, Communications of the Association for Computing Machinery, 4, 1961, 504-506.

• 02. On the construction of Bose-Chaudhuri matrices with the help of abelian group characters, Inst. Statist. Univ. North Carolina Mimeo Series no. 278, March 1961.

• 01. Sur quelques applications du problème d'Euler-Tarry à l'analyse de la variance, Thèse de doctorat de 3e cycle (Mathématiques Statistiques), Faculté des Sciences, Paris,1959.